Abstract
Adjoint methods have recently gained considerable importance in the finance sector, because they allow to quickly compute option sensitivities with respect to a large number of model parameters. In this paper we investigate how the efficiency of adjoint methods can be exploited to speed up the Monte Carlo-based calibration of financial market models. After analyzing the calibration problem both theoretically and numerically, we derive the associated adjoint equation and propose its application in combination with a multi-layer method, for which we prove convergence to a stationary point of the underlying optimization problem. Detailed numerical examples illustrate the performance of the method. In particular, the proposed algorithm reduces the calibration time for a typical equity market model with time-dependent model parameters from over three hours to less than ten minutes on a usual desktop PC.
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Kaebe, C., Maruhn, J.H. & Sachs, E.W. Adjoint-based Monte Carlo calibration of financial market models. Finance Stoch 13, 351–379 (2009). https://doi.org/10.1007/s00780-009-0097-9
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DOI: https://doi.org/10.1007/s00780-009-0097-9